Related papers: Heat Kernel methods in the first-order formalism
We compute the heat kernel for the Laplacians of symmetric transverse traceless fields of arbitrary spin on the $AdS$ background in even number of dimensions using the group theoretic approach introduced in \cite{Gopakumar:2011qs} and apply…
We prove sharp pointwise heat kernel estimates for symmetric Markov processes associated with symmetric Dirichlet forms that are local with respect to some coordinates and nonlocal with respect to the remaining coordinates. The main theorem…
We develop a method for solving the field equations of a quadratic gravitational theory coupled to matter. The quadratic terms are written as a function of the matter stress tensor and its derivatives in such a way to have, order by order,…
Kernel methods are powerful machine learning techniques which implement generic non-linear functions to solve complex tasks in a simple way. They Have a solid mathematical background and exhibit excellent performance in practice. However,…
The evaluation of effective potentials is critical for a range of phenomenological applications, including inflation, vacuum stability, and phase transitions. A drawback arises from the gauge-dependence of the effective potential.…
There has been recent progress in developing well-posed theories of relativistic viscous hydrodynamics and of gravitational effective field theories. These have in common the feature that they introduce unphysical degrees of freedom. We…
Dynamical generation of 4d gauge theories and gravity at low energy from the 3d ones at high energy is studied, based on the fermion condensation mechanism recently proposed by Arkani-Hamed, Cohen and Georgi. For gravity, 4d Einstein…
These lectures are an introduction to recent developments in the study of the high temperature phase of QCD by using weak coupling techniques. After a brief introduction to some techniques of quantum field theory at finite temperature, I…
Finite temperature quantum field theory in the heat kernel method is used to study the heat capacity of condensed matter. The lattice heat is treated a la P. Debye as energy of the elastic (sound) waves. The dimensionless functional of free…
We derive the asymptotic expansion of the heat kernel for a Laplace operator acting on deformed spheres. We calculate the coefficients of the heat kernel expansion on two- and three-dimensional deformed spheres as functions of deformation…
We obtain two-sided estimates for the heat kernel (or the fundamental function) associated with the following fractional Schr\"odinger operator with negative Hardy potential $$\Delta^{\alpha/2} -\lambda |x|^{-\alpha}$$ on $\RR^d$, where…
We present an effective four-dimensional formulation of the laws of gravity that respects the main features of a higher (five)-dimensional scenario of Randall-Sundrum type. The geometrical structure of the theory is that of a…
We use the boundary effective theory (BET) approach to thermal field theory in order to calculate the pressure of a system of massless scalar fields with quartic interaction. The method naturally separates the infrared physics, and is…
This is an introduction to the group field theory approach to quantum gravity, with emphasis on motivations and basic formalism, more than on recent results; we elaborate on the various ingredients, both conceptual and formal, of the…
In this paper, we study the geometry associated with Schroedinger operator via Hamiltonian and Lagrangian formalism. Making use of a multiplier technique, we construct the heat kernel with the coefficient matrices of the operator both…
This is the first paper in a series devoted to understanding the classical and quantum nature of edge modes and symmetries in gravitational systems. The goal of this analysis is to: i) achieve a clear understanding of how different…
In the monograph Renormalization and Effective Field Theory, Costello made two major advances towards the mathematical formulation of quantum field theory. Firstly, he developed an inductive position space renormalization procedure for…
In this article we develop a general method by which one can explicitly evaluate certain sums of $n$-th powers of products of $d\geq 1$ elementary trigonometric functions evaluated at $\mathbf{m}=(m_1,\ldots,m_d)$-th roots of unity. Our…
We apply the heat kernel method (using Avramidi's non-recursive technique) to the study of the effective action of chiral matter in a complex representation of an arbitrary gauge sector coupled to background U(1) supergravity. This…
Let $(X,d,\mu)$ be a $RCD^\ast(K, N)$ space with $K\in \mathbb{R}$ and $N\in [1,\infty]$. For $N\in [1,\infty)$, we derive the upper and lower bounds of the heat kernel on $(X,d,\mu)$ by applying the parabolic Harnack inequality and the…